The role of competing magnetic interactions in Mn-doped manganese antiperovskites Mn3+xA1−xN (A = Ni and Sn) has been explored using magnetometry and dilatometry, with particular focus on their relation to abnormal expansion properties. Rare negative magnetisation phenomena are found in zero-field-cooled conditions for both A = Sn and Ni when Mn is doped on the A site. Such behaviour is evidence of both competing magnetic sublattices and magnetocrystalline anisotropy. By comparison with other compounds with the antiferromagnetic magnetic structure, we suggest that competing interactions along with magnetovolume coupling influence the near-zero thermal expansion behaviour at intermediate temperatures below in the A = Ni family.